Question: Solve for $x$ and $y$ using elimination. ${x+4y = 24}$ ${-x+3y = 11}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $x$ and $-x$ cancel out. $7y = 35$ $\dfrac{7y}{{7}} = \dfrac{35}{{7}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {x+4y = 24}\thinspace$ to find $x$ ${x + 4}{(5)}{= 24}$ $x+20 = 24$ $x+20{-20} = 24{-20}$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {-x+3y = 11}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(5)}{= 11}$ ${x = 4}$